MacMahon's partition analysis XII

Plane partitions

George E. Andrews, Peter Paule

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

MacMahon developed partition analysis as a calculational and analytic method to produce the generating function for plane partitions. His efforts did not turn out as he had hoped, and he had to spend nearly twenty years finding an alternative treatment. This paper provides a detailed account of our retrieval of MacMahon's original project. One of the key results obtained with partition analysis is an extension of a theorem of Gansner which generalizes Stanley's famous trace theorem.

Original languageEnglish (US)
Pages (from-to)647-666
Number of pages20
JournalJournal of the London Mathematical Society
Volume76
Issue number3
DOIs
StatePublished - Jan 1 2007

Fingerprint

Plane Partitions
Partition
Trace Theorem
Generating Function
Retrieval
Generalise
Alternatives
Theorem

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

@article{52eea5567bed4d59a3e6a7d9d08895c9,
title = "MacMahon's partition analysis XII: Plane partitions",
abstract = "MacMahon developed partition analysis as a calculational and analytic method to produce the generating function for plane partitions. His efforts did not turn out as he had hoped, and he had to spend nearly twenty years finding an alternative treatment. This paper provides a detailed account of our retrieval of MacMahon's original project. One of the key results obtained with partition analysis is an extension of a theorem of Gansner which generalizes Stanley's famous trace theorem.",
author = "Andrews, {George E.} and Peter Paule",
year = "2007",
month = "1",
day = "1",
doi = "10.1112/jlms/jdm079",
language = "English (US)",
volume = "76",
pages = "647--666",
journal = "Journal of the London Mathematical Society",
issn = "0024-6107",
publisher = "Oxford University Press",
number = "3",

}

MacMahon's partition analysis XII : Plane partitions. / Andrews, George E.; Paule, Peter.

In: Journal of the London Mathematical Society, Vol. 76, No. 3, 01.01.2007, p. 647-666.

Research output: Contribution to journalArticle

TY - JOUR

T1 - MacMahon's partition analysis XII

T2 - Plane partitions

AU - Andrews, George E.

AU - Paule, Peter

PY - 2007/1/1

Y1 - 2007/1/1

N2 - MacMahon developed partition analysis as a calculational and analytic method to produce the generating function for plane partitions. His efforts did not turn out as he had hoped, and he had to spend nearly twenty years finding an alternative treatment. This paper provides a detailed account of our retrieval of MacMahon's original project. One of the key results obtained with partition analysis is an extension of a theorem of Gansner which generalizes Stanley's famous trace theorem.

AB - MacMahon developed partition analysis as a calculational and analytic method to produce the generating function for plane partitions. His efforts did not turn out as he had hoped, and he had to spend nearly twenty years finding an alternative treatment. This paper provides a detailed account of our retrieval of MacMahon's original project. One of the key results obtained with partition analysis is an extension of a theorem of Gansner which generalizes Stanley's famous trace theorem.

UR - http://www.scopus.com/inward/record.url?scp=44649160673&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=44649160673&partnerID=8YFLogxK

U2 - 10.1112/jlms/jdm079

DO - 10.1112/jlms/jdm079

M3 - Article

VL - 76

SP - 647

EP - 666

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

SN - 0024-6107

IS - 3

ER -